Panagiotis Rigas

Panagiotis Rigas, George Ioannakis, Ioannis Emiris

We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of constructing the diagram combinatorially, VoroFields learns a continuous, differentiable surrogate whose maximizer structure induces the partition implicitly. The Voronoi cells correspond to maximizer regions of the field, with boundaries defined by equal responses between competing sites. A hierarchical decomposition reduces the combinatorial complexity by refining only near envelope transition strata. Experiments across site families and metrics demonstrate accurate recovery of cells and boundary geometry without shape-specific constructions.

Christos Chatzisavvas, Panagiotis Rigas, George Ioannakis et al.

Slot-based object-centric learning represents an image as a set of latent slots with a decoder that combines them into an image or features. The decoder specifies how slots are combined into an output, but the slot set is typically fixed: the number of slots is chosen upfront and slots are only refined. This can lead to multiple slots competing for overlapping regions of the same entity rather than focusing on distinct regions. We introduce slot merging: a drop-in, lightweight operation on the slot set that merges overlapping slots during training. We quantify overlap with a Soft-IoU score between slot-attention maps and combine selected pairs via a barycentric update that preserves gradient flow. Merging follows a fixed policy, with the decision threshold inferred from overlap statistics, requiring no additional learnable modules. Integrated into the established feature-reconstruction pipeline of DINOSAUR, the proposed method improves object factorization and mask quality, surpassing other adaptive methods in object discovery and segmentation benchmarks.

Panagiotis Rigas, Panagiotis Drivas, Charalambos Tzamos et al.

We present \textbf{GARLIC}, a representation learning approach for Euclidean approximate nearest neighbor (ANN) search in high dimensions. Existing partitions tend to rely on isotropic cells, fixed global resolution, or balanced constraints, which fragment dense regions and merge unrelated points in sparse ones, thereby increasing the candidate count when probing only a few cells. Our method instead partitions \(\mathbb{R}^d\) into anisotropic Gaussian cells whose shapes align with local geometry and sizes adapt to data density. Information-theoretic objectives balance coverage, overlap, and geometric alignment, while split/clone refinement introduces Gaussians only where needed. At query time, Mahalanobis distance selects relevant cells and localized quantization prunes candidates. This yields partitions that reduce cross-cell neighbor splits and candidate counts under small probe budgets, while remaining robust even when trained on only a small fraction of the dataset. Overall, GARLIC introduces a geometry-aware space-partitioning paradigm that combines information-theoretic objectives with adaptive density refinement, offering competitive recall--efficiency trade-offs for Euclidean ANN search.